Number-theoretic methods in differential geometry

par Lam Pham (Ghent University)

jeudi 13 nov. 2025, 14:00 → 16:00 Europe/Paris

Margulis conjectured that torsion-free cocompact arithmetic lattices of semisimple Lie groups are uniformly discrete. Geometrically, this translates to a uniform lower bound on the lengths of all closed geodesics for arithmetic locally symmetric spaces. In joint work with M. Fraczyk, we proved that knowing that such a lower bound holds for arithmetic hyperbolic surfaces is enough to prove Margulis' conjecture for all higher rank simple Lie groups. Unconditionally, we also obtain uniform lower bounds on the lengths of ``most'' closed geodesics.